Answer
$\theta = 71^{\circ}$
Work Step by Step
We can use conservation of energy to find the increase in height of the center of mass from the vertical position to the maximum height:
$Mgh = 20~J$
$h = \frac{20~J}{Mg}$
$h = \frac{20~J}{(3.0~kg)(9.8~m/s^2)}$
$h = 0.68~m$
We can use geometry to find the angle $\theta$:
$cos~\theta = \frac{1.0~m-0.68~m}{1.0~m}$
$\theta = cos^{-1}~(\frac{0.32~m}{1.0~m})$
$\theta = 71^{\circ}$
